Seminar Event Detail


Algebraic Geometry

Date:  Thursday, November 10, 2016
Location:  B844 East Hall (3:10 PM to 4:00 PM)

Title:  On the unirationality of M_{1,n} in characteristic p.

Abstract:   We show that the Deligne-Mumford moduli space of genus 1 curves with n marked points is not unirational in characteristic p, for n sufficiently large with respect to p, when p>7. This statement, as well as the non-unirationality of many other Deligne-Mumford moduli spaces, was well-known in characteristic zero, but is more difficult in characteristic p. Our method uses the action of Frobenius on the etale cohomology of M_{1,n}. Following Deligne, we can compute this cohomology in terms of modular forms. The unirationality then follows from classical results on modular forms modulo p.

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Speaker:  Will Sawin
Institution:  Princeton/ETH

Event Organizer:     

 

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